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# Another DS from GMATPrep -- Absolute Value Inequalities

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Manager
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Another DS from GMATPrep -- Absolute Value Inequalities [#permalink]  10 May 2006, 14:31
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I don't really understand how to approach the inquality questions on the GMAT... any help on this question (and in general) from GMATPrep would be greatly appreciated...

Is lx-yl > lxl - lyl ?

(1) y < x
(2) xy < 0

Answer is B, but I don't understand it. Thanks for the help.

Marcus
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Joined: 06 May 2006
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For (1) y < x

a. if y > 0 and x > 0
then |x-y| = |x| - |y|

e.g. x = 5, y = 1. Evaluating, we get LHS = 4 and RHS = 4

b. if y < 0 and x > 0
then |x-y| > |x| - |y|

e.g. x = 5 and y = (-1). Evaluating, we get LHS = 6 and RHS = 4.

c. if y < 0 and x < 0
then |x-y| > |x| - |y|

e.g. x = (-1) and y = (-5). Evaluating, we get LHS = 4 and RHS = -4

So we cannot say for sure if the statement |x-y| > |x| - |y| will hold true given only condition (1).

For (2) xy < 0

a. y > x

if y > 0 and x < 0
then |x-y| > |x| - |y|

e.g. Taking y = 5 and x = -1 and evaluating, we get LHS = 6 and RHS = (-4).

b. y < x

if y < 0 and x > 0
then |x-y| > |x| - |y|

e.g. y = -5; x = 1. Evaluating, we get LHS = 6 and RHS = -4.

Hence for (2) we always get LHS > RHS i.e. |x-y| > |x| - |y|. Answer is (B).
GMAT Club Legend
Joined: 07 Jul 2004
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Actually I disagree with B.

It says xy < 0. Nothing in the question stem says x and y are both integers.

xy < 0 --> x and y are either:
(x = positive, y = negative)
If x = 3, y = -1, |x-y|=4, |x|-|y| = 2, |x-y| > |x|-|y|

(x = negative, y = negative)
If x = -2, y = 3, |x-y|=5, |x|-|y| = -1, |x-y| > |x|-|y|

(x and y are both positive fractions)
If x = 1/2, y = 1/4, |x-y|=1/2, |x|-|y|=1/4, |x-y| > |x|-|y|

(x and y are both negative fractions)
If x = -1/2, y = -1/4, |x-y| = 1/4, |x|-|y| = 1/4, |x-y| = |x|-|y|

In the last case, xy < 0, but |x-y| = |x|-|y|. So B should be insufficient.
Manager
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ywilfred wrote:
(x and y are both positive fractions)
If x = 1/2, y = 1/4, |x-y|=1/2, |x|-|y|=1/4, |x-y| > |x|-|y|

Wilfred, How is this condition upholding statement 2 where xy<0?
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5078
Location: Singapore
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Kudos [?]: 184 [0], given: 0

ywilfred wrote:
(x and y are both positive fractions)
If x = 1/2, y = 1/4, |x-y|=1/2, |x|-|y|=1/4, |x-y| > |x|-|y|

Wilfred, How is this condition upholding statement 2 where xy<0?

If x = 1/2,, y = 1/4, xy = 1/8 which is less than 0.
Manager
Joined: 29 Apr 2006
Posts: 85
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Kudos [?]: 11 [0], given: 0

ywilfred wrote:
ywilfred wrote:
(x and y are both positive fractions)
If x = 1/2, y = 1/4, |x-y|=1/2, |x|-|y|=1/4, |x-y| > |x|-|y|

Wilfred, How is this condition upholding statement 2 where xy<0?

If x = 1/2,, y = 1/4, xy = 1/8 which is less than 0.

Not meaning to be rude but xy=1/8 is not less than 0. In fact it is greater than 0. It is between 0 and +1.
If xy= -1/8 then, yes it would be less than 0.
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5078
Location: Singapore
Followers: 22

Kudos [?]: 184 [0], given: 0

ywilfred wrote:
ywilfred wrote:
(x and y are both positive fractions)
If x = 1/2, y = 1/4, |x-y|=1/2, |x|-|y|=1/4, |x-y| > |x|-|y|

Wilfred, How is this condition upholding statement 2 where xy<0?

If x = 1/2,, y = 1/4, xy = 1/8 which is less than 0.

Not meaning to be rude but xy=1/8 is not less than 0. In fact it is greater than 0. It is between 0 and +1.
If xy= -1/8 then, yes it would be less than 0.

haha.. i must be thinking too much. What a mistake !
VP
Joined: 29 Dec 2005
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Re: Another DS from GMATPrep -- Absolute Value Inequalities [#permalink]  10 May 2006, 19:17
lackeym77 wrote:
Is lx-yl > lxl - lyl ?

(1) y < x
(2) xy < 0

was discussed recently: http://www.gmatclub.com/phpbb/viewtopic ... ht=#197015
Re: Another DS from GMATPrep -- Absolute Value Inequalities   [#permalink] 10 May 2006, 19:17
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